What form waives the airline's liability in case of an entry refusal?

So, I was not offered this kind of form, and so cannot say what it's called.

However, regarding the actual issue: I called Qatar Airways's central hotline and explained my situation, whereby they put a note in the system "IN TRANSIT TO LONDON HOLDING A NATIONAL ID CARD. OK TO BOARD".

Despite having checked in online and printed my boarding pass, I went to the check-in desk 4 hours before departure to get a written confirmation to show gate staff, as I wasn't sure they'd have access to the system like the check-in staff.

After 30 minutes of bickering with a lady about whether I could travel, and insisting that she summon her supervisor, she eventually did. He checked the system for 3 minutes, eventually asking me "you go to London?" I said yes, whereby he said "wait" and called someone. Then, he printed out two fresh boarding passes and put a special stamp on the Tbilisi-Doha one (presumably similar to Ryanair's and Wizz's stamps indicating a non-EU passenger has been cleared), and told me I could go to the gate.

When I presented the documents at the gate, the agent scrutinised the stamped boarding pass for 20 seconds, before saying "OK, have a good flight".

That was the end of it - the rest of the trip was 100% painless.

There are two kinds of liability here.

First, the airline is liable to the government of the destination country if they bring the passenger which is obviously not admissible (such as not having proper documents for the destination). This liability is serious (monetary fines and possible suspension of operations). Thus in this case one should expect to be refused boarding, and I can't think of a case when anyone would offer to sign a form.

Second, there are cases when the passenger has the required paperwork, but the airline thinks there's a good chance the passenger would not be admitted. A good example is provided by @jpatokal above - having a passport with a valid visa, which shouldn't be issued. In this case the airline will not be fined, but still would be liable to fly the passenger back/onward as he won't be allowed entry. This will cost the airline extra (the return flight might be fully booked so someone has to be bumped), and while their contract of carriage usually already has provisions to charge you for those costs, they sometime bring a separate form for you to sign.

If you get this form: it would typically state that a) you have been warned and b) are aware that for [the reason they suspect] you may be refused entry, and c) in case of refused entry you agree to fly back on the airline's return flight and d) pay the full Y fare.

Why? There could be several reasons, although we can only guess (and the gate agent would just say "this is our standard procedure"):

• To further point out/remind that you are to spend some money if you're not allowed in - maybe in hope some people would get scared and decide not to board, letting the airline to make extra money by reselling your seat;

• To make it easier to legally collect money from you. If you bought your ticket from US, but flying from Doha to Georgia, and they'd bring you back to Doha, the contract signed in Doha would be easier to enforce there (it could, for example, state that the venue is in Doha). The court is also much more likely agree that you've read - and thus agreed - to this provision, comparing to regular "contracts of carriage", which nobody reads - and for which the airline even puts effort to make sure you wouldn't even want to read it.

So it turns out that Qatar Airways does have such a form, which is labeled "Indemnity Form: missing or insufficient travel documents," though it is unclear under what circumstances you'd be allowed to sign it and travel and under what circumstances you would be denied boarding, as airlines generally have legal obligations to governments to not transport passengers without the required documents. An airline cannot simply ignore these obligations by allowing passengers to sign a form, and so it is unlikely that the form would be offered to all passengers with questionable document situations.

A copy of the form is shown in this tweet, as some passengers were allegedly asked to sign them as part of this weekend's monumentally stupid, bigoted, and heartless (not to mention, at least as to some aspects, quite likely illegal) emergency change to US immigration policy. (Note that Qater Airways claims the forms were not used for this purpose this weekend. I offer it here as an example of the form's existence, not to cite any specific circumstance where it might or might not be used.)

As noted, there is no form waive liability. The airline could present you with an indemnification agreement, which is technically different. I've never seen nor even heard of one.

However, it's important to note that this happens all the time, the airline seeks indemnification for the cost of return by requiring return or onward tickets in some situations. But most of the time, they just accept the risk as the cost of doing business.

The thing is, if you expect the staff to 'misunderstand' transit requirements at DOH, a large transit hub, I would be a bit surprised if they even considered the existence of such a form.

Get there early enough to talk to a supervisor at check-in if there are any issues.